2000 character limit reached
Dissipative Soliton Resonance: Adiabatic Theory and Thermodynamics
Published 30 Apr 2023 in nlin.PS and physics.optics | (2305.00516v3)
Abstract: We present the adiabatic theory of dissipative solitons (DS) of complex cubic-quintic nonlinear Ginzburg-Landau equation (CQGLE). Solutions in the closed analytical form in the spectral domain have the shape of Rayleigh-Jeans distribution for a positive (normal) dispersion. The DS parametric space forms a two-dimensional (or three-dimensional for the complex quintic nonlinearity) master diagram connecting the DS energy and a universal parameter formed by the ratio of four real and imaginary coefficients for dissipative and non-dissipative terms in CQGLE. The concept of dissipative soliton resonance (DSR) is formulated in terms of the master diagram, and the main signatures of transition to DSR are demonstrated and experimentally verified. We show a close analogy between DS and incoherent (semicoherent) solitons with an ensemble of quasi-particles confined by a collective potential. It allows applying the thermodynamical approach to DS and deriving the conditions for the DS energy scalability.
- Ankiewicz, A., Akhmediev, N. (eds.): Dissipative Solitons. Springer, Berlin, German (2005) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Dissipative Solitons: from Optics to Biology and Medicine. Springer, Berlin, Germany (2008) Purwins et al. [2010] Purwins, H.-G., Bödeker, H., Amiranashvili, S.: Dissipative solitons. Advances in Physics 59(5), 485–701 (2010) Picozzi [2007] Picozzi, A.: Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. Optics Express 15, 9063–9083 (2007) Picozzi et al. [2014] Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Dissipative Solitons: from Optics to Biology and Medicine. Springer, Berlin, Germany (2008) Purwins et al. [2010] Purwins, H.-G., Bödeker, H., Amiranashvili, S.: Dissipative solitons. Advances in Physics 59(5), 485–701 (2010) Picozzi [2007] Picozzi, A.: Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. Optics Express 15, 9063–9083 (2007) Picozzi et al. [2014] Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Purwins, H.-G., Bödeker, H., Amiranashvili, S.: Dissipative solitons. Advances in Physics 59(5), 485–701 (2010) Picozzi [2007] Picozzi, A.: Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. Optics Express 15, 9063–9083 (2007) Picozzi et al. [2014] Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A.: Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. Optics Express 15, 9063–9083 (2007) Picozzi et al. [2014] Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. 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[2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. 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Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Purwins, H.-G., Bödeker, H., Amiranashvili, S.: Dissipative solitons. Advances in Physics 59(5), 485–701 (2010) Picozzi [2007] Picozzi, A.: Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. Optics Express 15, 9063–9083 (2007) Picozzi et al. [2014] Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A.: Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. Optics Express 15, 9063–9083 (2007) Picozzi et al. [2014] Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. 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Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Garnier, J., Hansson, T., Suret, P., S., R., G., M.: Optical wave turbulence: Towards a unified nonequilibrium thermodinamic formulation of statistical nonlinear optics. Phys. Reports 542, 1–132 (2014) Grelu and Akhmediev [2012] Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. 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Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. 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IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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[2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nature photonics 6(2), 84–92 (2012) Dudley et al. [2014] Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. 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IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Photonics 8(10), 755–764 (2014) Editorial [2014] Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Editorial: The power of analogies. Nature Photonics 8(1), 1 (2014) Kaup [1975] Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. 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[2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. 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(ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. 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Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. 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[2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kaup, D.: Exact quantization of the nonlinear Schrödinger equation. Journal of Mathematical Physics 16(10), 2036–2041 (1975) Lai and Haus [1989] Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. 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[2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. 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Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Lai, Y., Haus, H.: Quantum theory of solitons in optical fibers. ii. exact solution. Physical Review A 40(2), 854 (1989) Klaers et al. [2010] Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. 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[2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. 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Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. 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[2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Klaers, J., Schmitt, J., Vewinger, F., Weitz, M.: Bose–einstein condensation of photons in an optical microcavity. Nature 468(7323), 545–548 (2010) Sun et al. [2012] Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) 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[2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sun, C., Jia, S., Barsi, C., Rica, S., Picozzi, A., Fleischer, J.W.: Observation of the kinetic condensation of classical waves. Nature Physics 8(6), 470–474 (2012) Sob’yanin [2013] Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. 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[2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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[2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sob’yanin, D.N.: Bose-einstein condensation of light: General theory. Physical Review E 88(2), 022132 (2013) Bagnato et al. [2015] Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bagnato, V.S., Frantzeskakis, D.J., Kevrekidis, P.G., Malomed, B.A., Mihalache, D.: Bose-einstein condensation: Twenty years after. arXiv preprint arXiv:1502.06328 (2015) Kalashnikov and Wabnitz [2021] Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. 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Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. 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[2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. 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[1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Wabnitz, S.: A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a. Europhysics Letters 133(3), 34002 (2021) Bloch et al. [2022] Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. 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Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bloch, J., Carusotto, I., Wouters, M.: Non-equilibrium Bose–Einstein condensation in photonic systems. Nature Reviews Physics 4(7), 470–488 (2022) Chang et al. [2008] Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. 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Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. 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[2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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[2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Chang, W., Ankiewicz, A., Soto-Crespo, J., Akhmediev, N.: Dissipative soliton resonances. Physical Review A 78(2), 023830 (2008) van Saarloos and Hohenberg [1992] Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. 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JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. 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In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. 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[2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. 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[2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Saarloos, W., Hohenberg, P.: Fronts, pulses, sources and sinks in generalized complex ginzburg-landau equations. Physica D: Nonlinear Phenomena 56(4), 303–367 (1992) Haus et al. [1992] Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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[2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Haus, H.A., Fujimoto, J.G., Ippen, E.P.: Analytic theory of additive pulse and Kerr lens mode locking. IEEE Journal of quantum electronics 28(10), 2086–2096 (1992) Aranson and Kramer [2002] Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. 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Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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[1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Reviews of modern physics 74(1), 99 (2002) Ginzburg and Landau [2009] Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ginzburg, V.L., Landau, L.D.: On the Theory of Superconductivity, pp. 113–137. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-68008-6_4 . https://doi.org/10.1007/978-3-540-68008-6_4 Ferreira [2022] Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. 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[2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ferreira, M.F. (ed.): Dissipative Optical Solitons vol. 238. Springer, Cham, Switzerland (2022) Malomed [2005] Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. 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[2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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[2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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[2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.: Nonlinear Schrödinger equation, pp. 639–643. Taylor & Francis, New York (2005) Liu and Kengne [2019] Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. 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Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Liu, W.-M., Kengne, E.: Overview of Nonlinear Schrödinger Equations, pp. 1–13. Springer, Singapore (2019). https://doi.org/10.1007/978-981-13-6581-2_1 . https://doi.org/10.1007/978-981-13-6581-2_1 Carretero-González et al. [2008] Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Carretero-González, R., Frantzeskakis, D., Kevrekidis, P.: Nonlinear waves in bose-einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21(7), 139 (2008) Bale et al. [2008] Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bale, B.G., Kutz, J.N., Chong, A., Renninger, W.H., Wise, F.W.: Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers. JOSA B 25(10), 1763–1770 (2008) Leblond [2016] Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. 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[2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Leblond, H.: Dissipative solitons: The finite bandwidth of gain as a viscous friction. Physical Review A 93(1), 013830 (2016) Moores [1993] Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Moores, J.D.: On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Optics Communications 96(1-3), 65–70 (1993) Soto-Crespo et al. [1997] Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Soto-Crespo, J.M., Akhmediev, N.N., Afanasjev, V.V., Wabnitz, S.: Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion. Physical Review E 55(4), 4783 (1997) Renninger et al. [2008] Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W., Chong, A., Wise, F.: Dissipative solitons in normal-dispersion fiber lasers. Physical Review A 77(2), 023814 (2008) Pushkarov et al. [1979] Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. 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[2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Pushkarov, K.I., Pushkarov, D., Tomov, I.: Self-action of light beams in nonlinear media: soliton solutions. Optical and Quantum Electronics 11, 471–478 (1979) Yin and Lü [2023] Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. 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IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Yin, Y.-H., Lü, X.: Dynamic analysis on optical pulses via modified pinns: Soliton solutions, rogue waves and parameter discovery of the cq-nlse. Communications in Nonlinear Science and Numerical Simulation 126, 107441 (2023) Malomed and Nepomnyashchy [1990] Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A., Nepomnyashchy, A.A.: Kinks and solitons in the generalized Ginzburg-Landau equation. Physical Review A 42(10), 6009 (1990) Malomed [1987] Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. 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IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. 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Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Malomed, B.A.: Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations. Physica D: Nonlinear Phenomena 29(1-2), 155–172 (1987) Ankiewicz et al. [2007] Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N., Devine, N.: Dissipative solitons with a lagrangian approach. Optical fiber technology 13(2), 91–97 (2007) Ankiewicz and Akhmediev [2008] Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. 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JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ankiewicz, A., Akhmediev, N.: Comparison of lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 18(3), 033129 (2008) Podivilov and Kalashnikov [2005] Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. 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IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. 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[2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Podivilov, E., Kalashnikov, V.L.: Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation. Journal of Experimental and Theoretical Physics Letters 82, 467–471 (2005) Kalashnikov [2009] Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Kalashnikov, V.L.: Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. Physical Review E 80(4), 046606 (2009) Kalashnikov and Apolonski [2009] Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. 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IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Kalashnikov, V.L., Apolonski, A.: Chirped-pulse oscillators: A unified standpoint. Physical review A 79(4), 043829 (2009) Kharenko et al. [2011] Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Kharenko, D.S., Shtyrina, O.V., Yarutkina, I.A., Podivilov, E.V., Fedoruk, M.P., Babin, S.A.: Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg-Landau equation. JOSA B 28(10), 2314–2319 (2011) Kalashnikov [2017] Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Kalashnikov, V.L.: Optics and chaos: Chaotic, rogue, and noisy optical dissipative solitons. In: Skiadas, C.H., Skiadas, C. (eds.) Handbook of Applications of Chaos Theory, pp. 587–626. CRC Press, Boca Raton, USA (2017) Ablowitz and Horikis [2009] Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. 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[2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Ablowitz, M.J., Horikis, T.P.: Solitons in normally dispersive mode-locked lasers. Physical Review A 79(6), 063845 (2009) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-gibbsian stochastic light-mode dynamics of passive mode locking. Phys. Rev. Lett. 97, 113902 (2006) Kalashnikov [2009] Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. 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[2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. 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[2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. 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New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. 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[2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Chirped solitary-pulse solutions of the complex completely cubic-quintic nonlinear Ginzburg-Landau equation. Maple worksheet http://dx.doi.org/10.13140/RG.2.1.4375.6886 (2009) Bleistein and Handelsman [1975] Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. 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Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. 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[2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. 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[2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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[2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Ardent Media, NY, USA (1975) Wu et al. [2019] Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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[2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wu, F.O., Hassan, A.U., Christodoulides, D.N.: Thermodynamic theory of highly multimoded nonlinear optical systems. Nature Photonics 13(11), 776–782 (2019) Brabec et al. [1992] Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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[2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Brabec, T., Spielmann, C., Curley, P., Krausz, F.: Kerr lens mode locking. Optics letters 17(18), 1292–1294 (1992) Rudenkov et al. [2023] Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Rudenkov, A., Kalashnikov, V.L., Sorokin, E., Demesh, M., Sorokina, I.T.: High peak power and energy scaling in the mid-ir chirped-pulse oscillator-amplifier laser systems. Opt. Express 31(11), 17820–17835 (2023) https://doi.org/10.1364/OE.484742 Kalashnikov et al. [2005] Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Kalashnikov, V.L., Podivilov, E., Chernykh, A., Naumov, S., Fernandez, A., Graf, R., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment. New Journal of Physics 7(1), 217 (2005) Sorokin et al. [2022] Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Sorokin, E., Rudenkov, A., Kalashnikov, V., Sorokina, I.: Atmospheric dispersion management in the mid-ir mode-locked oscillators. arXiv preprint arXiv:2212.00909 (2022) Kalashnikov et al. [2011] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Chirped dissipative soliton absorption spectroscopy. Optics Express 19(18), 17480–17492 (2011) Akhmediev et al. [2008] Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Akhmediev, N., Soto-Crespo, J.M., Grelu, P.: Roadmap to ultra-short record high-energy pulses out of laser oscillators. Physics Letters A 372(17), 3124–3128 (2008) Kolner [1994] Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kolner, B.H.: Space-time duality and the theory of temporal imaging. IEEE Journal of Quantum Electronics 30(8), 1951–1963 (1994) Kalashnikov [2018] Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. 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[2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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[2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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[2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Kalashnikov, V.L.: Theory of laser energy harvesting at femtosecond scale. In: Harooni, M. (ed.) High Power Laser Systems, pp. 173–196. IntechOpen, London, UK (2018) Picozzi et al. [2009] Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Picozzi, A., Barviau, B., Kibler, B., Rica, S.: Thermalization of incoherent nonlinear waves: From incoherent solitons to a thermodynamic description of statistical nonlinear optics. The European Physical Journal special topics 173(1), 313–340 (2009) Zakharov et al. [2012] Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin-Heidelberg, Germany (2012) Robinson [1997] Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Robinson, P.: Nonlinear wave collapse and strong turbulence. Reviews of modern physics 69(2), 507 (1997) Renninger et al. [2010] Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Renninger, W.H., Chong, A., Wise, F.W.: Area theorem and energy quantization for dissipative optical solitons. JOSA B 27(10), 1978–1982 (2010) Katz et al. [2006] Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Katz, M., Gordon, A., Gat, O., Fischer, B.: Non-Gibbsian stochastic light-mode dynamics of passive mode locking. Physical review letters 97(11), 113902 (2006) Kalashnikov et al. [2003] Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Kalashnikov, V.L., Sorokin, E., Sorokina, I.T.: Multipulse operation and limits of the kerr-lens mode-locking stability. IEEE journal of quantum electronics 39(2), 323–336 (2003) Rotschild et al. [2008] Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Rotschild, C., Schwartz, T., Cohen, O., Segev, M.: Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photonics 2(6), 371–376 (2008) Dragoman [1997] Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Dragoman, D.: I: The wigner distribution function in optics and optoelectronics. In: Progress in Optics vol. 37, pp. 1–56. Elsevier, Rochester, N.Y. U.S.A (1997) Düring et al. [2009] Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Düring, G., Picozzi, A., Rica, S.: Breakdown of weak-turbulence and nonlinear wave condensation. Physica D: Nonlinear Phenomena 238(16), 1524–1549 (2009) Wan et al. [2023] Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Wan, Z., Wang, H., Liu, Q., Fu, X., Shen, Y.: Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photonics (2023) Gat et al. [2005] Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005) Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
- Gat, O., Gordon, A., Fischer, B.: Light-mode locking: a new class of solvable statistical physics systems. New Journal of Physics 7(1), 151 (2005)
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